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Projekt Do kariery na skrzydłach – studiuj Aviation Management Projekt współfinansowany ze ś rodków Europejskiego Funduszu Społecznego. Biuro projektu: Wyższa Szkoła Informatyki i Zarządzania z siedzibą w Rzeszowie ul. Sucharskiego 2, 35-225 Rzeszów 2 We used OLS method to develop an equation to describe the quantitative dependence between Y and X. Although the least squares method results in the line that fits the data with minimum distances, the regression equation is not a perfect predictor, unless all observed data points fall on the predicted regression line. We cannot expect all data points to fall exactly on the regression line. The regression line serves only as an approximate predictor of a Y value for a given value of X (or given values of X 1, X 2, …, X k ). Therefore, we need to develop a statistic that measures the variability of the actual values from the predicted Y values. The differences between an observed Y value and the Y value predicted from the sample regression equation ( ) is called a residual. residual for i-th observation actual value of Y for i-th observation estimated value of the dependent variable using regression equation (simple or multiple) for i-th observation

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Projekt Do kariery na skrzydłach – studiuj Aviation Management Projekt współfinansowany ze ś rodków Europejskiego Funduszu Społecznego. Biuro projektu: Wyższa Szkoła Informatyki i Zarządzania z siedzibą w Rzeszowie ul. Sucharskiego 2, 35-225 Rzeszów 8 The measure of variability around the line of regression is called the standard error of the estimate (or estimation). It measures the typical difference between the actual values and the Y values predicted by the regression equation. This can be seen by the formula for the standard error of the estimate: standard error of the estimate sample Y values values of Y calculated from the regression equation sample size number of predictors It is measured in units of the dependent variable Y. STANDARD ERROR OF THE ESTIMATE IS A MEASURE OF THE VARIABILITY, OR SCATTER, OF THE OBSERVED SAMPLE Y VALUES AROUND THE REGRESSION LINE.

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Projekt Do kariery na skrzydłach – studiuj Aviation Management Projekt współfinansowany ze ś rodków Europejskiego Funduszu Społecznego. Biuro projektu: Wyższa Szkoła Informatyki i Zarządzania z siedzibą w Rzeszowie ul. Sucharskiego 2, 35-225 Rzeszów 15 HOW GOOD IS OUR MODEL? In order to examine how well the independent variable (or variables) predicts the dependent variable in our model, we need to develop several measures of variation. The first measure, the TOTAL SUM OF SQUARES (SST), is a measure of variation (or scatter) of the Y values around the mean. The total sum of squares can be subdivided into explained variation (or REGRESSION SUM OF SQUARES, SSR), that is attributable to the relationship between the independent variable (or variables) and the dependent variable, and unexplained variation (or ERROR SUM OF SQUARES, SSE), that which is attributable to factors other than the relationship between the independent variable (or variables) and the dependent variable.

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Projekt Do kariery na skrzydłach – studiuj Aviation Management Projekt współfinansowany ze ś rodków Europejskiego Funduszu Społecznego. Biuro projektu: Wyższa Szkoła Informatyki i Zarządzania z siedzibą w Rzeszowie ul. Sucharskiego 2, 35-225 Rzeszów 21 coefficient of determination,R 2 The coefficient of determination, R 2, of the fitted regression is defined as the proportion of the total sample variability explained by the regression and is and it follows that R 2 gives the proportion of the total variation in the dependent variable explained by the independent variable ( or variables ). If R 2 = 1, then ???If R 2 = 0, then ???

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Projekt Do kariery na skrzydłach – studiuj Aviation Management Projekt współfinansowany ze ś rodków Europejskiego Funduszu Społecznego. Biuro projektu: Wyższa Szkoła Informatyki i Zarządzania z siedzibą w Rzeszowie ul. Sucharskiego 2, 35-225 Rzeszów 22 coefficient of indetermination, The coefficient of indetermination,, of the fitted regression is defined as the proportion of the total sample variability unexplained by the regression and is and it follows that gives the proportion of the total variation in the dependent variable unexplained by the independent variable ( or variables ). If its equal to 1, then ???If its equal to 0, then ???

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Projekt Do kariery na skrzydłach – studiuj Aviation Management Projekt współfinansowany ze ś rodków Europejskiego Funduszu Społecznego. Biuro projektu: Wyższa Szkoła Informatyki i Zarządzania z siedzibą w Rzeszowie ul. Sucharskiego 2, 35-225 Rzeszów 23 adjustedcoefficient of determination,R 2 The adjusted coefficient of determination, R 2, is defined as We use this measure to correct for the fact that non-relevant independent variables will result in some small reduction in the error sum of squares. Thus the adjusted R 2 provides a better comparison between multiple regression models with different numbers of independent variables. Since R 2 always increases with the addition of a new variable, the adjusted R 2 compensates for added explanatory variables. or

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Projekt Do kariery na skrzydłach – studiuj Aviation Management Projekt współfinansowany ze ś rodków Europejskiego Funduszu Społecznego. Biuro projektu: Wyższa Szkoła Informatyki i Zarządzania z siedzibą w Rzeszowie ul. Sucharskiego 2, 35-225 Rzeszów 24 coefficient of multiple correlation The coefficient of multiple correlation, is the correlation between the predicted value and the observed value of the dependent variable: and is equal to the square root of the coefficient of determination. We use R as another measure of the strength of the linear relationship between the dependent variable and the independent variable ( or variables ). Thus it is comparable to the correlation between Y and X in simple regression.

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Projekt Do kariery na skrzydłach – studiuj Aviation Management Projekt współfinansowany ze ś rodków Europejskiego Funduszu Społecznego. Biuro projektu: Wyższa Szkoła Informatyki i Zarządzania z siedzibą w Rzeszowie ul. Sucharskiego 2, 35-225 Rzeszów 26 coefficient of determination should be calculated as follows: The coefficient of determination should be calculated as follows: coefficient of indetermination: Its easy to provide the coefficient of indetermination: IT CAN BE SAID THAT 29% OF THE VARIABILITY IN HOME SIZES (Y) REMAINS UNEXPLAINED BY THE FAMILY INCOME. THEREFORE, 71% OF THE VARIABILITY IN HOME SIZE S (Y) IS EXPLAINED BY THE PREDICTOR. WE HAVE ACCOUNTED FOR 71% OF THE TOTAL VARIATION IN THE HOME SIZES BY USING INCOME AS A PREDICTOR OF HOME SIZE.

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Projekt Do kariery na skrzydłach – studiuj Aviation Management Projekt współfinansowany ze ś rodków Europejskiego Funduszu Społecznego. Biuro projektu: Wyższa Szkoła Informatyki i Zarządzania z siedzibą w Rzeszowie ul. Sucharskiego 2, 35-225 Rzeszów 28 coefficient of determination should be calculated as follows: The coefficient of determination should be calculated as follows: coefficient of indetermination: Its easy to provide the coefficient of indetermination: IT CAN BE SAID THAT 18,6% OF THE VARIABILITY IN WEEKLY SALARY (Y) REMAINS UNEXPLAINED BY LENGTH OF EMPLOYMENT (X1) AND THE AGE (X2) OF EMPLOYEES. THEREFORE, 81,4% OF THE VARIABILITY IN WEEKLY SALARY (Y) IS EXPLAINED BY THESE TWO PREDICTORS.

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